Related papers: The Cuba Library
The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…
We consider the classical problem of computing the expected value of a real function $f$ of the $d$-variate random variable $X$ using cubature formul\ae. We use in synergy tools from Commutative Algebra for cubature rul\ae, from elementary…
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) $\Delta^0_\alpha$ bi-embeddable categoricity, and degrees of…
We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree…
We discuss how quantum information distribution can improve the performance of some quantum computation tasks. This distribution can be naturally implemented with different types of quantum cloning procedures. We give two examples of tasks…
We present the CosmoBolognaLib, a large set of Open Source C++ numerical libraries for cosmological calculations. CosmoBolognaLib is a living project aimed at defining a common numerical environment for cosmological investigations of the…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
High-quality visualizations are an essential part of robotics research, enabling clear communication of results through figures, animations, and demonstration videos. While Blender is a powerful and freely available 3D graphics platform,…
Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete…
This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and…
The connection and eventual integration of High-Performance Computing (HPC) with Quantum Computing (QC) represents a transformative advancement in computational technology, promising significant enhancements in solving complex, previously…
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in \cite{LSX}. The main results consist of a new derivation of the Gaussian type cubature for the…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in…
Research progress in quantum computing has, thus far, focused on a narrow set of application domains. Expanding the suite of quantum application domains is vital for the discovery of new software toolchains and architectural abstractions.…
QDax is an open-source library with a streamlined and modular API for Quality-Diversity (QD) optimization algorithms in Jax. The library serves as a versatile tool for optimization purposes, ranging from black-box optimization to continuous…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…